Some Curvature Properties of ( LCS ) n - Manifolds
نویسندگان
چکیده
and Applied Analysis 3 aR (X, Y) ξ + b [S (Y, ξ)X − S (X, ξ) Y +g (Y, ξ) QX − g (X, ξ) QY] − τ n [ a n − 1 + 2b] [g (Y, ξ)X − g (X, ξ) Y] = 0. (24) Here, taking into account of (16), we have [η (Y)X − η (X)Y] [a (α 2 − ρ) + b (n − 1) (α 2 − ρ) − τ n ( a n − 1 + 2b)] + b [η (Y]QX − η (X)QY] = 0. (25) Let Y = ξ be in (25); then also by using (18) we obtain [−X − η (X) ξ] [a (α 2 − ρ) − τ n ( a n − 1 + 2b) + b (n − 1) (α 2 − ρ) ] + b [−QX − η (X) (n − 1) (α 2 − ρ) ξ] = 0. (26) Taking the inner product on both sides of the last equation by Y, we obtain [g (X, Y) + η (X) η (Y)] [a (α 2 − ρ) + b (n − 1) × (α 2 − ρ) − τ n ( a n − 1 + 2b)] + b [S (X, Y) + η (X) η (Y) (α 2 − ρ) (n − 1)] = 0, (27) that is,
منابع مشابه
ACTION OF SEMISIMPLE ISOMERY GROUPS ON SOME RIEMANNIAN MANIFOLDS OF NONPOSITIVE CURVATURE
A manifold with a smooth action of a Lie group G is called G-manifold. In this paper we consider a complete Riemannian manifold M with the action of a closed and connected Lie subgroup G of the isometries. The dimension of the orbit space is called the cohomogeneity of the action. Manifolds having actions of cohomogeneity zero are called homogeneous. A classic theorem about Riemannian manifolds...
متن کاملOn Stretch curvature of Finsler manifolds
In this paper, Finsler metrics with relatively non-negative (resp. non-positive), isotropic and constant stretch curvature are studied. In particular, it is showed that every compact Finsler manifold with relatively non-positive (resp. non-negative) stretch curvature is a Landsberg metric. Also, it is proved that every (α,β)-metric of non-zero constant flag curvature and non-zero relatively i...
متن کاملCommutative curvature operators over four-dimensional generalized symmetric spaces
Commutative properties of four-dimensional generalized symmetric pseudo-Riemannian manifolds were considered. Specially, in this paper, we studied Skew-Tsankov and Jacobi-Tsankov conditions in 4-dimensional pseudo-Riemannian generalized symmetric manifolds.
متن کاملConformal mappings preserving the Einstein tensor of Weyl manifolds
In this paper, we obtain a necessary and sufficient condition for a conformal mapping between two Weyl manifolds to preserve Einstein tensor. Then we prove that some basic curvature tensors of $W_n$ are preserved by such a conformal mapping if and only if the covector field of the mapping is locally a gradient. Also, we obtained the relation between the scalar curvatures of the Weyl manifolds r...
متن کاملOn Lorentzian two-Symmetric Manifolds of Dimension-four
‎We study curvature properties of four-dimensional Lorentzian manifolds with two-symmetry property‎. ‎We then consider Einstein-like metrics‎, ‎Ricci solitons and homogeneity over these spaces‎‎.
متن کاملOn Geometry of Submanifolds of (LCS)n-Manifolds
The geometry of manifolds endowed with geometrical structures has been intensively studied, and several important results have been published. In this paper, we deal with manifolds having a Lorentzian concircular structure LCS n-manifold 1–3 see Section 2 for detail . The study of the Lorentzian almost paracontact manifold was initiated by Matsumoto in 4 . Later on, several authors studied the ...
متن کامل